Limits to ductility set by plastic flow localization

The theory of strain localization is reviewed with reference both to local necking in sheet metal forming processes and to more general three dimensional shear band localizations that sometimes mark the onset of ductile rupture. Both bifurcation behavior and the growth of initial imperfections are considered. In addition to analyses based on classical Mises-like constitutive laws, approaches to localization based on constitutive models that may more accurately model processes of slip and progressive rupturing on the microscale in structural alloys are discussed. Among these non-classical constitutive features are the destabilizing roles of yield surface vertices and of non-normality effects, arising, for example, from slight pressure sensitivity of yield. Analyses based on a constitutive model of a progressively cavitating dilational plastic material which is intended to model the process of ductile void growth in metals are also discussed. A variety of numerical results are presented. In the context of the three dimensional theory of localization, it is shown that a simple vertex model predicts ratios of ductility in plane strain tension to ductility in axisymmetric tension qualitatively consistent with experiment, and the destabilizing influence of a hydrostatic stress dependent void nucleation criterion is illustrated. In the sheet necking context, and focussing on positive biaxial stretching, it is shown that forming limit curves based on a simple vertex model and those based on a simple void growth model are qualitatively in accord, although attributing instability to very different physical mechanisms. These forming limit curves are compared with those obtained from the Mises material model and employing various material and geometric imperfections